Why has physics failed to completely explain the universe: a philosophical approach to a final theory
by
JOHN FREDERICK THOMPSON
submitted in accordance with the requirements for the degree of
DOCTOR OF PHILOSOPHY
In the subject
PHILOSOPHY
at the
UNIVERSITY OF SOUTH AFRICA
SUPERVISOR: Prof C D Scott CO-SUPERVISOR: Prof E Rapoo
25 July 2023
DECLARATION
I declare that:
“Why has physics failed to completely explain the universe: a philosophical approach to a final theory”
is my own work and that all the sources that I have used or quoted have been indicated and acknowledged by means of complete references.
I further declare that I submitted the thesis to originality checking software. The result summary is attached.
I further declare that I have not previously submitted this work, or part of it, for examination at UNISA for another qualification or at any other higher education institution.
John Frederick Thompson 26th January 2023
Abstract: English
WHY HAS PHYSICS FAILED TO COMPLETELY EXPLAIN THE UNIVERSE: A PHILOSOPHICAL APPROACH TO A FINAL THEORY
This thesis investigates why there is still no ‘final’ physical theory of the universe despite the enormous resources involved. Current physical and philosophical methodologies are examined leading to a new strategy. The history of knowledge from mythology to the present day is traced to establish the general nature and psychology of human sapience and group dynamics. This reflects strongly on human common sense, education and entrenchment caused by peer pressure of mathematical and physical ideas. Arguments consider physical and philosophical standpoints of empirical versus rational and mathematical versus non-mathematical deduction. The former is decided by introducing a special foundational philosophy; the latter by arguing the universe has no need of mathematics in any form to exist. Criticizing current ideas is useless unless they can be replaced by a better theory. As a paradigm must be better than that which it replaces, it must stand up to testing against observation. Using the concept of time with a clear definition, possibly the first such definition, shows how a universe must causally develop. The human concept of space, together with a reason for its 3-dimensionality, automatically arises to answer, ‘if a universe is to be created, into what is it placed?’ The conundrum of existence is also explained. The reason for contemporary physics’ failure is its reliance on observation, which is governed by unreliable human perception, in particular its lack of definitions for time, length, mass, electric charge, energy, work, wave function from which its ‘laws’ are deduced. Doubt is raised on physics’ main theories, quantum mechanics and relativistic field theories which deny a fundamental cause for the universe. Mathematics suffers from overconfidence in its efficacy and accuracy. There also exist processes that the foundational theory shows are completely hidden from current physical and astrophysical experiments. The conclusion to be drawn is that mathematical physics cannot produce a final theory whereas non-mathematical reasoning can. Foundational philosophy then becomes the means of attaining a final theory with physics the method of determining philosophy’s accuracy. As no such pointer has been considered in the literature it has to be a testable primary assumption. Lines for further research to produce a complete theory of the universe are given.
Keywords: Theory of Everything, Cosmology, Quantum theory, Causality, Ontology, Epistemology, Mathematical Platonism, Mathematical obscurity, Mensuration, Empiricism, Definition, Group/peer pressure, Entrenchment, Common sense.
Opsomming: Afrikaans
HOEKOM HET FISIKA NIE DIE HEELAL VERKLAAR NIE: AFILOSOFIESE BENADERING TOT 'N FINALE TEORIE
Hierdie tesis ondersoek hoekom daar steeds geen 'finale' fisiese teorie van die heelal is ten spyte van die enorme hulpbronne wat betrokke is. Huidige fisiese en filosofiese metodologieë word ondersoek wat lei tot 'n nuwe strategie. Die geskiedenis van kennis vanaf mitologie tot vandag word nagespeur om die algemene aard en sielkunde van menslike weelde en groepdinamika vas te stel. Dit reflekteer sterk op menslike gesonde verstand, opvoeding en verskansing wat veroorsaak word deur groepsdruk van wiskundige en fisiese idees. Argumente oorweeg fisiese en filosofiese standpunte van empiriese teenoor rasionele en wiskundige versus nie-wiskundige afleiding. Eersgenoemde word besluit deur 'n spesiale grondliggende filosofie in te voer; laasgenoemde deur te redeneer die heelal het geen behoefte aan wiskunde in enige vorm om te bestaan nie. Om huidige idees te kritiseer is nutteloos, tensy dit deur 'n beter teorie vervang kan word. Aangesien 'n paradigma beter moet wees as dit wat dit vervang, moet dit standhou tot toetsing teen waarneming. Die gebruik van die konsep van tyd met 'n duidelike definisie, moontlik die eerste so 'n definisie, wys hoe 'n heelal oorsaaklik moet ontwikkel.
Die menslike konsep van ruimte, tesame met 'n rede vir sy 3-dimensionaliteit, ontstaan outomaties om te antwoord 'as 'n heelal geskep moet word, waarin word dit geplaas?' Die raaisel van bestaan word ook verduidelik. Die rede vir kontemporêre fisika se mislukking is sy vertroue op waarneming wat beheer word deur onbetroubare menslike persepsie, veral sy gebrek aan definisies vir tyd, lengte, massa, elektriese lading, energie, werk, golffunksie waaruit sy 'wette' afgelei word. Twyfel word geopper oor fisika se hoofteorieë, kwantummeganika en relativistiese veldteorieë wat 'n fundamentele oorsaak vir die heelal ontken. Wiskunde ly aan oorvertroue in die doeltreffendheid en akkuraatheid daarvan. Daar bestaan ook prosesse wat die grondliggende teorie toon heeltemal verborge is van huidige fisiese en astrofisiese eksperimente. Die gevolgtrekking wat gemaak moet word, is dat wiskundige fisika nie 'n finale teorie kan produseer nie, terwyl nie-wiskundige redenering wel kan.
Fundamentele filosofie word dan die middel om 'n finale teorie te bereik met fisika die metode om filosofie se akkuraatheid te bepaal. Lyne vir verdere navorsing om 'n volledige teorie van die heelal te produseer, word gegee.
Isicatshulwa: isiXhosa
KUTHENI I-FIZIKSI ISILELE UKUCACISA INDALO YONKE:INDLELA YOPHANDO-LWAZI NGOBUNJANI NENTSINGISELO YOBUKHO BEZINTO
UKUSA KWITHIYORI YOKUGQIBELA
Le thisisi iphanda ukuba kutheni kungekabikho ithiyori yendalo iphela nangona zizininzi izixhobo ezisetyenziswayo. Iindlela zangoku zokwemvelo nezefilosofi ziyavavanywa ukuze kufikelelwe kwisicwangciso-qhinga esitsha.
Imbali yolwazi ukusuka kwizifundo ngeentsomi ukuza kuthi ga ngoku iyalandelwa ukuze kusekwe imeko yendalo ngokubanzi nemeko yobulumko bengqondo bomntu kunye nenkqubo yokuziphatha kunye neenkqubo zengqondo ezenzeka ngaphakathi kweqela. Oku kubonakalisa ngamandla/ngokukuko kwindlela yokucinga komntu, imfundo kunye nokuzinza okubangelwa luxinzelelo loontanga kwiingcamango zemathematika kunye nezendalo.
Iingxoxo zithathela ingqalelo iimbono zendalo nezefilosofi zamava achasene nengqiqo kunye nemethamatika ngokuchasene nokunciphisa ekungeyoyamethametika. Eyokuqala igqiba ngokwazisa ifilosofi eyodwa esisiseko; ze engeyokugqibela igqibe ngokuxoxa ukuba indalo iphela ayifuni imathematika nangaluphi na uhlobo ukuze ibekho.Ukugxeka iingcamango zangoku akuncedi nto ngaphandle kokuba zinokuthatyathelw’ indawo yithiyori engcono kunazo.Njengoko iphatheni/
imodeli(paradigm) kufuneka ibengcono kunaleyo inqwenela ukuba ithathe indawo yayo, kufuneka ikumele ukuvavanywa ngokwemigqaliselo ngokokuqwalasela. Inkcazo ecacileyo yengcamango yexesha, ekunokwenzeka yingcaciso yokuqala enjalo, ibonisa indlela indalo ekhula ngayo ngokuzenzekelayo. Ingcamango yomntu yesithuba/ indawo ejikeleze ihlabathi, kunye nesizathu sobukhulu bayo ngokobuthathu, iwuphendula ngokuzenzekelayo umbuzo othi ‘ukuba indalo iphela iza kuyilwa, ibekwe kwintoni?’ Uqashi qashi wobukho ucacisiwe. Isizathu sokungaphumeleli kwefiziksi yanamhlanje ukuchaza indalo kukuxhomekeka kwayo ekuqwalaseleni, okulawulwa yimbono yabantu engathembekanga kwaye, ngokukodwa, ukusilela kwayo kwiinkcazo zexesha, ubude, ubunzima, ubungakanani bombane, amandla, umsebenzi, kunye nomsebenzi wamaza apho 'imithetho' isekelwe/ ithathwa khona. Amathandabuzo abekwa kwiithiyori eziphambili zefiziksi, ubungakanani bobuxhakaxhaka obufunekayo kunye neethiyori eziphikisa ukuba kukho unobangela osisiseko wendalo iphela. IMathematika inengxaki yokuzithemba ngokugqithisileyo kumandla ayo okusebenza nangokuchaneka kwayo. Ithiyori yesiseko ibonisa ukuba iinkqubo ezithile zangoku zifihlwe ngokupheleleyo kwimifuniselo ngokobunzululwazi bezemvelo nokwakheka kweenkwenkwezi.
Isigqibo sesokuba ifiziksi (ubunzululwazi ngezinto zemvelo ezingaphiliyo) yemathematika ayinakwakha /ayinakuyila ithiyori egqibeleleyyo ngelixa ukuqiqa okungengokwemathematika
kunokukwenza oko. Ifilosofi esisiseko ngoko iba yindlela yokuseka ithiyori yokugqibela ze ifiziksi ibe yindlela yokumisela ukuchaneka kwefilosofi. Ekugqibeleni, kucetyiswa imikrwelo/izihloko zophando zokuqhubela phambili uphando ngenjongo yokuvelisa ingcamango/ ithiyori epheleleyo ngendalo iphela .
Acknowledgements
Professor C. D. Scott, not only for his guidance and support as supervisor but for his initial warm response to my request to commence PhD studies.
Professor E. Rapoo, as co-supervisor, for her invaluable comments which led to many interesting diversions into the analysis of mathematical methodology and peer group dynamics.
And not least my daughter for her suggestion to take my early ideas forward, her great help with my non-existent computer knowledge, and general academic advice; and my wife who has done everything possible to give me time to work flat out, not only to write, but also to read the vast amount of literature on both the physical universe and philosophy as well as ancillary subjects such as education, genetics, biochemistry, mythology and group dynamics. I owe her more than I can ever say.
CONTENTS
Declaration i
Abstract (English) ii
Keywords ii
Abstract (Afrikaans) iii
Abstract (isiXhosa) iv
Acknowledgements vi
Table of Contents vii
Glossary x
Preamble 1
CHAPTER 1 Introduction 2
1.1 Background 2
1.1.1 Physical review 3
1.1.2 A brief review of mathematics from a physical perspective 5
1.1.3 The role of Philosophy 10
1.1.4 Philosophy v physics 13
1.2 Fundamental problem and objectives 17
1.3 Methodology 18
1.3.1 Methodology questions 22
1.3.2 Methodology – strategy 28
1.3.3 Some intractable problems of expression 30
1.4 Significance 32
1.5 Summary of central themes 33
1.6 Structural outline 33
CHAPTER 2 The shape of human reason 36
2.1 Introduction 36
2.2 The Beginnings and group mentality 36
2.3. Philosophy 43
2.4 Mathematics 50
2.5 Physics 62
2.5.1 Education 72
2.5.2 common sense 73
2.5.3 Entrenchment 76
2.6 Brief summary of Chapter 2 77
CHAPTER 3 A thought experiment in Time 79
3.1 Introduction 79
3.1.1 The fundamental principles of the arguments 81
3.1.2 A philosophy for causality? 81
3.1.3 Metaphysics, a philosophy of what? 87
3.2 Measurement 91 3.3 Towards a fundamental premise 96 3.3.1 The fundamentals of universal being 96 3.3.2 Time and existence 98
3.3.3 Towards a definition for time 103 3.4 Definition of Time 105 3.5 On reality 107
CHAPTER 4 Foundational philosophy 115
4.1 Introduction 115
4.2 Into what can a Universe be put? 115
4.3 Recordability 117
4.4 Concepts of space and no space 122
4.4.1 Rotation and units of Time 126
4.5 Three dimensions and the simple building module of space 135
4.6 Form of trace-points 143
4.7 Expanding Space-Time 144 4.8 Special relativity 148 4.8.1 Considerations arising from Einstein’s special theory (1905) 148
4.8.2 FitzGerald contraction 157 4.8.3 Spatially separated simultaneity 158 4.8.4 General principle of two-way observation between two observers 160 4.8.5 Muon lifetime 164 4.8.6 Minkowski 4-dimensional spacetime 164 4.8.7 Relativistic dynamics and rotation 165
4.8.8 Simultaneity revisited 166 4.8.9 Final note 168
4.9 Into what can a universe be put and human perception of space 169 4. 10 Summary of sections 4.5-4.6 173 4.11 The governing, or foundational, rule of the Universe in Euclidean terms 174 CHAPTER 5 Macrospace 176 5.1 Introduction 176 5.2 Standard Theory of the creation 177 5.3 Philosophical issues 183
5.4 The fundamental Universe 187
5.5 Contraction and expansion epochs 191
5.6 Conservation of energy 193
5.7 The human concept of Space 193
5.8 The existence of Time and earth. 194
5.9 Hermeneutics 196
CHAPTER 6 Conclusion 200
6.1 Introduction 200
6.1.1 Overview 200
6.2 Fulfilment of Aims and Objectives 202
6.2.1 Ramifications, revolutions, and ‘firsts’ 205
6.3 Common sense 206
6.4 Further research 207
6.4.1 Philosophy 207
6.4.2 Physics 208
6.5 The motivational problem of Chapter 1 209
Bibliography 212
List of Figure
Figure 2.1. Wave-forms 51
Figure 4.1 A p-rotating point 132
Figure 4.2 Transformation of natural space-Time to Euclidean plane 137
Figure 4.3 Different representations of space-Time 140
Figure 4.4 Space-Time generation 147
Figure 4.5 Four generations of space-Time 149
Figure 4.6 Motion of light-wave along a rod 151
Figure 4.7 Comparison of two observers 155
Figure 4.8 Lorentz-FitzGerald contraction 158
Figure 4.9 Relativistic contraction 163
Figure 5.1 Universal expansion of space-Time 189
Figure 5.2 -Cartesian dimensional space-Time 190
Figure 5.3 Figure 5.2 projected onto plane 191
Glossary
photon that carries off excess energy, particularly in the visible spectrum
photon responsible for forced interactions especially for ‘electric force’
+ The rotation of the relativistic universe
¯ The fundamental rotation of the natural universe
The starting point of the universe
Replaces + in the macro-universe description
A spin required to keep the two representations of the universe in balance
c Speed of light
c* Rate of creation of space-Time
f frequency instead of v (nu) to distinguish it from velocity v.
CMB, CMBR Cosmic microwave background (radiation)
EPR Einstein, Podolski, Rosen paper on completeness of quantum mechanics Flip The change in orientation of a neutron to proton
Free axis A development direction that leads directly to space-Time lattice points GR Einstein’s theory of general relativity
LQG Loop quantum gravity
N The set of all natural numbers
N The set of Time numbers contained in the natural numbers Natural universe The universe outside of space-Time – the point universe
P-rotation A name used to distinguish a fundamental form of rotation which, by being fundamental, cannot be described in more fundamental terms. It leads directly to an exact definition for rotation.
QFT Quantum field theory
QHM, QHO Quantum Harmonic motion/oscillation
QM Quantum mechanics
qul quantum unit of length; 1 qul = 1.77041 10-15 m qut quantum unit of time; qut as 4.175785 10-24 s Relativistic universe The universe consisting of space-Time intervals SHM, SHO Simple harmonic motion /oscillation
T
Time creating operation – rotation operator.
TA Age of the universe
Triad A set of three orthogonal axes
Triple-triad A group of three triads formed into a rotating space-Time volume (particle)
Trace-point A point created in the space-Time lattice
w The maximum possible rotation of, or in, the universe
The following mathematical terminology is used.
21/2 = square root of 2. 2-1/2 = 1/square root of 2. 1024 = 1 followed by 24 zeros = 1 million million million million; 10-9 = 1/1000 000 000; 10-9 m = 1 nanometre or nm; ms-1 = metre per second in SI units, m2 = square metre etc; dimensional terms T= time, M = mass, L = length, T -1 = per time unit.
Speed is given in lower script, velocity, speed with direction, in bold. Time (capital T) is a vector quantity so never considered as a scalar.
Preamble
67 years ago, I was taught “We know that everything is made of protons, neutrons and electrons, but we do not know what those are made of”. That set me on a course of thought: If I was God what single thing could I say that would lead to a universe? After a few suggestions to my physics master, I was told to stop reading advanced books (I had none) and concentrate on my schoolwork. A couple of years later I heard of Einstein and Quantum mechanics and thought that my ideas had already been discovered so buried the matter, although I was still interested in certain problems like, how big could the universe be or become? 35 years later when my daughter was at university, a chance remark led her to suggest I should develop my original ideas further. I did so taking into account relativistic field theory. There, I discovered the Higgs problem noting that his equations had no mass term which had led him to deduce that certain expressions they contained counted for the mass term as a separate particle. However, a different idea occurred to me. Could it be that the imposition of a relativistic expression in field theory was so strong that it removed terms such as mass and electric charge; that is, could relativity be showing that really, instead of four fundamental entities (space, time, mass and charge) only two were actually necessary for a natural, or a theistic, cause to create a universe? Then immediately a further step suggested itself: If this was the case, why stop at two dimensions, space, and time? Could it not be that only one of these (space or time) might provide a basic cause for the universe?
CHAPTER 1 Introduction
1.1 Background
The theory of how the universe functions, and why it exists, has been developing over thousands of years from purely mythological concepts, through general philosophy, gradually fostering more practical ideas, and eventually rigorous physical theories based on observation. Leaving aside mythology, Aristotle’s ([350 BCE] 1923) original philosophy aimed at discovering the first causes of existence, and the universal structure, but these were purely deductive philosophy rather than based on experiment. Consequently, the introduction of experiment, or testing of theory, by Bacon (1605) and Galileo (1632) towards the end of the Renaissance period, showed up falsities in the earlier interpretations of the world. The result was a rise of experiment and change from Aristotelian metaphysics to scientific reasoning based on observation, while imposing suspicion on common sense and reducing the role of reasoning (Feyerabend 1993:291; Sankey 2010; Yu & Cole 2014:679).
Nevertheless, the structure and existence of the universe has become a subject that is no longer limited to scholars but is now of great interest to the public at large, as suggested by the number of television programs screened.
However, despite the huge resources thrown at it, no complete, or ‘final’ theory of the structure and processes of the universe has been uncovered. If these are known they should surely lead to a much improved set of living conditions for not only humans but for all of Earth itself. Consequently, it seems essential to delve deeply into the concepts and methods of physics to find, firstly, a pointer on why physics has so far failed in its quest for a theory of everything, and secondly, to obtain pointers on why we may need another completely new approach and exactly what this should be.
This thesis is concerned with those arguments pertaining to, or directed at, establishing a final, or complete, theory of the structure of the universe. That is, a final theory should be a complete description of the fundamental structure and processes giving rise to any universe. Preliminary research determined, after considering contemporary physical ideas, that such a theory must be heavily reliant on philosophical concepts. Consequently, an aim will be to use these arguments to point the way to a theory that relies only on pure philosophical reasoning, by which I mean sapient thought based on the principle ‘if A then B must follow’; which suggests an initial single principle for an original starting point.
The background for this chapter is thus divided into three main areas of review: physics, mathematics, and the role of philosophy. For this review physics is taken as specifically the human interpretation of the concepts of ‘matter’ and ‘energy’, their form, properties, and interactions with regard to our observed surroundings1. Mathematics is taken as “The study of numbers, measurements and space; a science dealing with the measurement, properties and relationship of quantities …”2,3 Philosophy: “ … the study of the principles of all real knowledge, study of the most general causes and principles of the universe: …”2.
1.1.1 Physical review
The last hundred years has seen advances and exchange of knowledge in the physics of the universe increase at an almost exponential rate; not only through the ability to construct ever larger and more powerful telescopes (e.g., Hubble and Keck) and research equipment, (e.g., the CERN accelerator) but through the introduction of computers enabling viciously difficult calculations to be carried out in seconds and information transferred equally fast. Indeed, this thesis could not have been created without such technology. Despite the huge resources, including humans, the attainment of an all- encompassing theory seems as far away as ever as more and more problems appear with every observation (Witten 2005:1085).
The basis of physics, the structure of matter and how it forms the universe, passes back to the ancient Greeks and earlier. Even now this basis is not clear. Physics asserts four fundamental entities space, time, mass, and electric charge, none of which are defined. Of these, mass is believed to be somehow responsible for gravitation; and charge for the properties of attraction and repulsion between particles, causing them to bind into specific forms. But the actual constitution, what is, how and why questions of these effects, is still unknown. Quantum mechanics (QM) and quantum field theory (QFT) have arisen as an attempt to explain respectively the concept of matter including mass, and its interactions including electromagnetism. These theories produce some seemingly absurd ideas concerning the reality of existence itself, for which a major concern is the ‘rejection of reality’ by both theories (Schrödinger 1935:3, Penrose 2004:507, Rees 1987:46, d’Espagnat 1979:158, and argued against by Einstein, Podolsky and Rosen (1935) (EPR). Here, one must consider the meaning of reality in terms of human concepts. To some extent this subsumes the human feeling of solidness, concreteness and ‘material being’ created by the ability to touch. In this sense the question must be asked whether quantum physicists have thought far enough to overcome their idea that the world is made of objects that cannot be considered real (comment attributed to Bohr, [Leggett 2002:419]) and
1 World Book Dictionary 1989. cf Oxford Reference 2015, Cambridge Advanced English 2020 .
2 World Book Dictionary 1989.
3 Some physicists e.g., Tegmark (2007) have considered mathematics to be the foundation of the universe itself.
now adopted as a QM principle. This and allied concepts become ‘problems’ when physics is confronted by human common sense. As a result, common sense becomes an interface between science, philosophy, and education with a commonly held view that, as above, human common sense is unreliable (Yu and Cole 2014:680, Maxwell 1966:295), it being based at best upon both human perceptions and interpretations of our surroundings. This will necessitate clarification as there may be more than one interpretation to each perception.
To quantum theories should be added Einstein’s ([1916]1923) General Relativity (GR). Much of the last ninety years has been spent trying to correlate this to quantum theories. GR, as with most relativistic field theories, is mathematically so complex that only the simplest solutions have so far been obtained, providing ideas for exploration rather than confident conclusions. A possibility of coordinating the two (GR and QM) has recently arrived, loop quantum gravity (LQG), but this, too, has its problems; it requires reforming some sacrosanct physical concepts (e.g., spacetime continuum see Chapter 4). If these problems could be overcome allowing QM and GR to be amalgamated, it would be a major step in producing the so-called ‘theory of everything’ (TOE) – a combining theory of the four forces thought to rule the universe, the electromagnetic force, gravity, the strong and weak nuclear forces – also called the grand unification theory (Peskin and Schroeder 1995:§22.2).
However, the question must be asked whether such a combination would present a complete, or final, theory which overarches all processes of the universe. Ellis (2012:27), for example, states that physical laws cannot answer ultimate questions on themselves – why they exist or are they complete (see EPR 1935). This is equivalent to stating that no theory can prove itself. It must therefore be capable of being tested outside of itself (Popper 2006) – a somewhat difficult process in QM as QM refutes the concept of any local reality (EPR-Bell 1964). As a result, doubt may arise whether an overarching theory can ever be reached and of what form it may take. An interesting article in Nature (2005) surveying eleven physicists gives three hopeful of success: Weinberg, Smolin, Stachel; six reserving judgement: Ellis, Randall, Fukugita, ’t Hooft, Witten, Susskind; and two believing such a theory is far off: Rovelli and Penrose. Baumgarten (2017) argues that such a theory will arise through clarifying existing physical theories. Of those quoted in Nature (2005) only Ellis expresses real doubts concerning this, while Rovelli and Penrose believe that, like EPR something is missing. Ellis later called for a conference on “the wildly speculative nature of modern physics theories” (in Wolchover 2015). None of these scientists appeared to consider that perhaps a totally new approach might be necessary. (String theory, not considered in this treatise, is approximately 50 years old [Greene 2000:136]). But Baumgarten (2017:2) points out that if the final theory arises under current conditions, then it has to be a tautology, it will add nothing new. He also rules out (2017:2) “like Weinberg” (section 1.1.3) that any such theory can be derived by reason alone. It can only come from fully explained physical laws, (2017:4, 11 [contradicted by Feyerabend 1993:291]).
But, as foreseen by Ellis (2012:28), physical content must destroy a final theory’s truth value: as he points out, equations are limited to predictions, especially as they are built around limited knowledge of local observation about particular rather than general problems – “conditional statements” (Wigner 1960:7). Eddington (1928:141) puts it that science constructs a world symbolic of “commonplace experience”, which can be misleading and thus not necessarily truthful to the underlying structure. So, as with Feyerabend (1993:291), we must consider that physics is “not sacrosanct.” It “may have basic faults” and be “in need of global change”. Furthermore, Ellis (2012:27) suggests that physicists cannot create experiments that answer the metaphysical questions – the current laws must be explained, particularly in terms of a basic universal law which itself requires an explanation why it should exist. Perhaps the most valid comment is that by Hossenfelder (2020) in
“Why the foundations of physics have not progressed for 40 years” – new methods are needed with greater care over financing research.
These thoughts compel questioning of physical methodology. The views of Einstein (1916:221) and Dirac (1940:122) have shaped the direction of such thought and research over the last sixty years.
They reflect exactly ‘the state of the game’ at present. The physicist determines by experimental means the measurements of the universe that give values according to human systems of measuring units. He then determines the assumptions that will allow interpretation of these results, assuming them to be generally representative of every part of the universe. From these he formulates rules, or laws, that combine the experimental results into predictive equations. He performs further experiments to ascertain whether the rules he has imagined are correct. The basis of his research then becomes measurement, that is, mathematically structured valuation based on some human system of measuring units. The process will thus be human perception → measurement → interpretation. In this view, observation, and only observation, forms the basis of physical laws which themselves form human scientific knowledge of the universe (Stenger 2015:1-4; Einstein 1933;274).
Both Einstein (1936:324 and Dirac (1940:124) are clear that the laws of nature are to be expressed mathematically. Consequently, the relation of mathematics, not only to physics, but more importantly to the human psyche should be considered, because that must play a role in the methodology adapted.
1.1.2 A brief review of mathematics from a physical perspective
We prove propositions, theories and lemmas in mathematics, but do we explain in mathematics? (Persson 2011:2).
It is all very well to explore mathematical theory to extremes, but one should keep in mind the question whether these theories fit the universe and explain its fundamentals; or are these explorations more of a mathematical game or challenge to human sapience?
Mathematics is said to be formed on a set of truths or axioms based on the concept of number.
Fundamentally numbers are measurement. We all count, learning the symbols 1, 2, 3 … . In essence, these are all built on the form 1 meaning singularity – thus: 1; 1,1; 1,1,1; which humans have defined as one, two, three, three being larger than two or one, and so on. These can be split to 1; (1,1); (1,1),1;
so that 3 is an association of 1 and 2 together. Then four would be two lots of 2, and so on. We can also employ the symbols + and , and by inference – (subtraction), and then include the reciprocal function to or multiplication as or division. From these simple definitions we can build up some axioms such as the transitive theorem: if A implies B and B implies C, then A implies C. Or the commutative theorem: if A and B are two simple numbers then A+B = B+A, or AB = BA. These are basically self-evident truths. If all mathematics is derived from these and other such conditions it should be unequivocal and computations derived from them should be true.4 As mathematics has developed, some of these rules must be carefully amended to cover the developments, for example in matrix theory where if A and B are matrices AB is not commutable in general. As this have both philosophers and mathematicians assiduously examined all, I shall go no further into this subject (Hilbert [1899] 1950; Russell [1903] 2019; Gödel 1931; Zach 2019).
From these simple axioms, deductive reasoning can be used to prove theorems. In a sense these could be considered as a game of logic taught early on at school using geometry, for example, the theorems of Pythagoras. This is an approach which has led to the assumption becoming ingrained in educated people that all deductively reasoned mathematics is true. As Brown (2008:2,60-62) points out, mathematical (logical) proof equals certainty, such mathematics has yet to find an exception and this on-going accuracy is a reason for our belief. Consequently, once proven a mathematical theorem lasts forever. Furthermore, as mathematics develops, always through logical arguments, new rules are based on unequivocal definitions. In theory, such mathematics should be truthful to itself, and where errors occur it is due to incorrect application or human error. I shall not go into the philosophical concept of ‘nominalism’ on the existence and abstractness of mathematical objects other than to say that the abstractness of so-called Platonic mathematics, being independent of other structures, should not be muddled with abstraction as in abstract art – drawing out of ideas from concrete observation.
Mathematical abstractness should be taken as being not concrete in the sense of not having material
4 Allowing for Gödel’s incompleteness theorem that says given an axiomatic mathematical system it is always possible to find unanswerable questions or even statements that can be both proved and disproved. This is similar to saying no theory can prove itself, or deriving the liar paradox that if a liar says he is lying, is he lying or not?
existence. However, the subject of Platonism is important as it appears to sharpen the belief in favour of mathematical arguments supplying the fundamental concepts of universal structure, in particular those of quantum mechanics and field theory.
Many mathematicians are Platonists (Abbott 2013:2148) meaning that mathematics is akin to Plato’s belief in certain divine concepts in the construction of the world. Plato’s discovery of abstract objects corresponds to a view that mathematics is an autonomous discipline whose concepts are abstract entities, existing independently of time, space, humans, and the physical world (Brown 2008:61, Linnebo (2009:1), Colyvan 2011:88, Bueno 2013:§1, section 1.3.1 (i) ). It would be the same for any universe that might exist as Nunez (1999:48) points out. This is virtually the opposite of the quantum mechanical views that the universe is not independent of humans!5 The platonic view could mean that, as Brown (2008:61) suggests: “Mathematics is a priori, not empirical”, and (2008:14) he notes that no physical result has ever overturned any mathematical calculation. Linnebo (2009:1), for example believes mathematics is discovered, not invented, which perhaps fits in with Lappas and Spyrou (2003:2) that it is genetically embodied in the human brain. Certainly, humans seem to have a predilection for number and measurement. The thought that numbers were first in the world tracks back at least to the Pythagoreans (Aristotle [350BCE] 1923:bookA§6), although Aristotle himself remarked at the end of book N that “objects of mathematics … are not the first principles”.
The use of mathematics over the last century has developed rapidly in its complexity. It invades every part of human life. The usefulness of mathematics to physics, is not in doubt (see e.g. Hughes 1985:40-59; Brown 2004:59; Colyvan 2001:116).6 Specifically, Einstein (1933:274) stated that mathematics is necessary to construct and express nature’s laws with nature being “the simplest that is mathematically conceivable”, echoed by Wigner (1960:1-14) who refers to its effectiveness in promoting physical theories as “mysterious”: “...the laws of nature must have been formulated in the language of mathematics to be an object for the use of applied mathematics.”
Through the work of Einstein and Dirac inter alia (e.g., Maxwell 1865), mathematics has been taking an ever-increasing role in the hunt for an all-encompassing theory of the universe based on the proposition that it may be mathematical in creation (Dirac 1940, Tegmark 2007). At the very least, mathematics is regarded by many physicists and mathematicians as the only way in which any theory
5 Views discussed by many mathematicians and philosophers. See e.g., Lappas and Spyrou (2003), Nunez, Edwards and Matos (1999), Quine (1951), Putnam (1975) among many more including those already mentioned. For further reading see bibliography.
6 Locke ([1690] 1999:556) wrote “… the reality of mathematical knowledge. I doubt not but it will be easily granted.”
of the universe can be expressed (e.g., Baumgarten 2017:1, Penrose 2005:18 as well as others already mentioned). Its ability to underlie the human construction of rules to predict conclusions – and formulate rules such as Maxwell’s electromagnetic equations (cf Krauss 1984) – has had a massive impact on advancing physical theory and has been treated at length from the philosophical view by many philosophers (Kuhn 1970 and Cartwright 1983:5, 11). It has even shaped new physical ideas:
Dirac (Field theory 1927), Pauli (Neutrino 1930), Yukawa (mesons 1935), giving it an apparently eternal quality as though it is the basis of everything (Lappas and Spyrou 2003). Indeed, mathematics’
rhythmical undertones can be perceived in music, art, and advertising. (Bhat, Wani and Anees 2015, Tubbs 2014, Gamwell 2015).
I should state here these are the views of physicists and mathematicians. I put the views in as forthright way as possible without arguing about their truth or falsity – that will come later. In any case, it is hard to find any sensible contrary statements. The adopted implication, then, is that there is a clear-cut affinity between the laws and structure of the universe with mathematics – taken to the extreme by Tegmark (2007). Hamming (1980:82) in a similar essay writes “Constantly, what we predict from the manipulation of mathematical symbols is realized in the real world.”
Tegmark (2007) believes that the universe is purely mathematical. “There exists an external physical reality completely independent of us humans” or any other sapient beings; and “Our external physical reality is a mathematical structure.” How this would work is not clear as the mathematical formalism does not exist at this stage; rather it is a collection of theories, but he points out ideas that might eventually produce reduction to a single overarching fundament. His concept is very similar to Aristotle’s philosophy (see Chapter 2) of trying to find a first principle by analysing human thought structures from the general to the particular. Tegmark (2007) considers various forms such as scalars, vectors and tensors, or rotations and translations, being functions of a simpler structure – what mathematicians call an irreducible representation – one which can have no greater commonality.
Further, he believes it should be possible to reduce measurements (units of scale) to a commonality, that is, to pure number form. To some extent he puts his finger on a problem of observation. Our universe is complicated in that we see the large picture composed of enormous groupings of minute entities forming their own group structures. Consequently, it is extremely difficult to work back to the real underlying fundamental structure. (This will be seen in the following chapters even down to
‘hidden from us’ factors).
Clearly, physicists believe mathematics works for them and provides answers to properly constructed questions. Here properly constructed means clearly defined input for, as computer analysts say, rubbish in – rubbish out! It is also here that we must be careful because ‘applied’
mathematics, that is, physical mathematics whether it is for astrophysics, rocketry, industry et cetera,
depends on its applicability. So, while mathematics may be seen as true, it depends very much on its interpretation and usage when applied outside of itself. The question might even be asked whether some of the more recondite mathematics might be beyond any requirement of a mathematical description of the universe. Have these advanced concepts arisen because of themselves, meaning that they are muddying the waters of far simpler explanations?
From these few paragraphs it therefore seems clear that mathematics is heavily entrenched in the human psyche and particularly in physics. Humans are logical (on the whole!) and thus prefer logical objectivity. Nevertheless, the question should be asked whether mathematics should be the totality of physical research. Under Platonism it is regarded as being independent of humanity, that is, not shaped by human intuition, whereas human sapience depends on perception of our surroundings. Is this fixation on mathematics, then, in the best interests of human deduction? Does it inhibit thoughts outside the ‘box’? Humans should have been asking: (1) to what extent is this apparent usefulness of mathematics self-centred; (2) whether it could possibly be at the root of the universe; and (3), if not (2), what is the root of both mathematics and the universe?
There thus arises the concept of other human views, that is, through philosophical reason or logic.
For example, I take the view that mathematical results are founded entirely on hypotheses that are formed by the human mind, and therefore, mathematics should not be taken as an absolute truth of natural causes in relation to the actuality of the universe. As expressed by Kuhn (1970) and others, there may be different explanations that fit the original problems. Testing these hypotheses is an established principle, but again to what extent may other explanations, such as those founded on philosophy, prove acceptable or even better? This, after all, must be based on the structure and processes of the universe because the human mind has grown out of the universe.
It seems to me the fundamental problem with theoretical physics (the mathematical expression of cosmology – taking cosmology as the fundamental structure of the universe including its basic elements) is its empirical nature building on observation, which, in its theories, has led to its empirical nature becoming self-contradictory. On the one side it uses human observations built up over the centuries entrenching them through their use to formulate physical laws. On the other side, mathematically based theories such as quantum mechanics have produced ideas that conflict strongly with human perception. As already mentioned, Bohr is famous for his attributed statement that the universe is made of things that are not real (Leggett 2002:419); while (d’Espagnat 1979:158, Rees 1987:46, and Mermin 1981:397) claim the universe is dependent on humans for its existence.7 The use of observation must then be considered an important problem with physical explanations because
7 Actual quotations given in section 2.5.
it may overlook hidden fundamental causes that are beyond current human comprehension. In short, physics, mathematical or otherwise, cannot be relied upon to give an accurate assessment of the fundamental structure of the universe (cf Hossenfelder’s (2020) objection above). So it is to philosophy that I now turn, to the philosophy of science and metaphysics. From the aspect of an overall theory of the universe it will prove valuable to consider contemporary views of these subjects – views that have developed with the advance of physics. However, I shall only take those concepts relevant to attaining a final theory.
1.1.3 The role of Philosophy
For if we do not at least know what a thing is, how can we talk or think comprehendingly about it? (Lowe, 2021: 5.)
Contemporary philosophy has its basis in ancient Greek discourse about everything that mattered around or affected human life. The branch that deals with science matters is defined in dictionaries severally as the speculative rather than observational use of reasoning about the fundamental nature of the real world, existence, and limits of knowledge.8 The difference to science is that science relies on testing of observation by experiment whereas philosophy, sometimes referred to disparagingly as armchair physics, relies on pure thought and discourse over variant views. The part of interest, the fundamentals of nature and existence, has so far been considered as metaphysics, ‘the after the physics’, as ascribed by Andronicus of Rhodes to the series of Aristotle’s works, the books A-N (alpha to nu) [350BCE](1923). As suggested by the title, these followed Aristotle’s “Physics”, books I-VIII [350BCE](1991), in which he laid the foundation of what was to become the subject of science.
In his metaphysics Aristotle analysed observation by classification of general concepts to specifics, and vice versa, in the hope of finding the reason for their existence which he considered a superior knowledge to merely knowing what those observables were or did. From this classification he hoped to find the most fundamental principles “universals” governing the world around him: “the hardest for men to know; for they are farthest from the senses” (1923:A1). These principles then become the most important knowledge as everything else follows from these. (A point I will argue, particularly with respect to QM, which eschews causality, throughout this thesis raising the subject of a methodology for an investigation process, which follows in section 1.3.1 onwards).
8 Combinations of philosophy definitions retrieved 19th May 2022 from:
Cambridge English Dictionary, Cambridge University Press https: //dictionary.cambridge.com
OED, Oxford University Press https: //www.oed.com, Merriam-Webster https: //www.merriam-webster.com
However, Callender (2011:2) and van Inwagen & Sullivan (2014§1) find metaphysics no longer has a clear definition following a recent move that metaphysics should be concerned with “developing generalizations” from physical theories and should not be in the business of attempting to formulate physics rules. This is clearly like the philosophers Ladyman and Ross (2007) ‘naturalized metaphysics’ and is I believe, most certainly putting the ‘cart before the horse’, for the latest scientific theories are the most controversial leading to numerous peculiarities as mentioned above. Ladyman and Ross accept and even argue by using the peculiar views (non-reality) of quantum mechanics as a basis for rejection of metaphysical argument. For example, they write: “a first approximation to our [naturalistic] metaphysics is: ‘There are no things. Structure is all there is.’” (2007:130) They argue that this principle has been established by successful QM tests. Maudlin (2007:1) seems to agree:
The basic idea is simple: metaphysics, insofar as it is concerned with the natural world, can do no better than to reflect on physics. Physical theories provide us with the best handle we have on what there is, and the philosopher's proper task is the interpretation and elucidation of those theories.
French and McKenzie (2012:44) accept the arguments for naturalized (naturalistic) metaphysics but rather see a role for traditional metaphysics in the same context as pure mathematics to physics – mathematics defining to physics what is acceptable. The last view is better, but still not, I feel, the full use of philosophical reasoning. Reasoning is to develop by logical argument, and to question ideas that appear illogical (such as existence depending on ‘unreal’ objects) and to provide alternatives.
The Ladyman and Ross arguments are that metaphysicians do not consider ‘hows’ as opposed to science which does; metaphysis only asks ‘what’ by analysing semantic categories (2007:21).
Consequently, standard metaphysics has contributed nothing to contemporary knowledge (2007:vii) and if it is to have any use it should be dependent on science (an idea also evident in Russell (1913:6)), as science provides the best theories available. However, it seems to me this ignores a fundamental concern of metaphysics: the exploration of existence itself. Such a revelation would surely be of an immense value to attaining an overall theory of the universe. But then Ladyman and Ross believe structure (‘structuralism’) is the only reality. Thus, they assume (2007:310) they have defended realism, adding “For example, when people consider whether God created reality, they have deflated reality so as to allow for there to be something more”. (But is realism just a structure created out of human attempts to find the basis of our universe?)
As a result (2007:259) Ladyman and Ross agree Russell’s rejection of causality on the basis physicists do not seek causes and therefore it would be improper for metaphysicians to say they should. They place causality as an “artefact of an anthropocentric perspective that science supersedes”
(2007:260,267) and add “If this possibility obtains, the metaphysician is justified in studying physics in search of universal glue, but causation cannot itself be that glue.” Surely this is the total entrenchment of an extraordinarily blinkered view?
But then the arguments of Ladyman and Ross do seem to leave something to doubt. They (2007:16) point out areas where metaphysical ideas have proved completely false in the past. This is as ridiculous as blaming physics for many of its original views, such as electricity being a liquid, or inflammable objects containing a quantity of fire. Ideas come and go as knowledge advances.
Ladyman and Ross should rather consider the possibility of philosophy developing new ideas outside the limits of current thought, whether these be physical or philosophical.
Having given one view of philosophy I will give a brief synopsis of an alternative they attack (2007:15-16).
Lowe (2002) follows Aristotle’s view that metaphysics deals with the deepest questions of ‘being’
or existence, together with the essential nature of knowing about existence, to know about the universal structure. He considers metaphysics should be used as a science with its “epistemic basis [similar to] mathematics and logic” by using “ontological categories” like Aristotle, whose influence can be seen in Lowe’s statement (2002:11) that “the real essences of material substances are known to those who talk or think comprehendingly about such substances”.
Lowe is not alone: Fine (2014:8) states “Metaphysics is concerned, first and foremost, with the nature of reality” and the nature of things – what they are (2014:10); it is distinguished by its generality compared to other philosophies dealing with particulars – like Lewis’s supervenience theory. Lewis (1986:25-46 and 1996:549-567) tacitly suggests that humans believe a reality depending on the point of view of the beholder at a given time; to obtain the fundamental truth one reduces the concept to a common goal. But this in fact shows that such a method cannot arrive at the truth because it always depends on human perception. So therefore, we cannot ever arrive at a metaphysically general truth by any human method. We can only speculate at a possible truth or first cause. In any case there may exist several possible foundational principles so that an assumption to the truthful one is the only possible method of genesis.
Aristotle’s metaphysics explores, among other things, the notion that philosophy should deal with the concept of truth in relation to theoretical knowledge – the aim of theoretical knowledge being truth (1923: A1). Such an enquiry will depend on a combination of discovering the nature of different objects, finding a possible first cause of everything (1923 A2) and the principles for determining such a cause (B6). It will have to deal with existence (B2 on) and being (books D1-2, H and Z) which must
include consideration of abstract (for example love) as well as material things. (The abstract will feature at the most important level in this thesis). Aristotle introduced the concept of classification from universals to particular, like phyla unfolding to species in biological classification. Also included in Book Z is the important concept of definition which I will argue is a major failing of physical theory.
Thus, Aristotle’s metaphysics deals primarily with discovering the nature of things (abstract or substantial), existence and being, and finally the fundamental cause of everything, and principles behind the cause. I shall take the opposite view that the cause is the originator of the universe which leads to the principles and nature of its existence; that is, discovering the cause will lead to why anything should be in existence.
In my view, a valuable contribution on the question of metaphysics, and that of philosophy in general, is that of Stenlund (2003) that the question of its rationale is always “perpetually present” to discussion. Physics is based upon sometimes disconnected observations or experiments; therefore, it is dangerous that philosophy of science should be based upon it when philosophy in its ancient frame was to determine the basis of our world. According to Campbell and Jeffreys (1938:133) philosophers are more interested in theories than physical laws, which is as it should be, because the laws are surely the result of something fundamental that perhaps observation, and thus empiricism cannot uncover?
The fundamentals should then give the laws. Philosophy is supposed to find the problems in physics (de Haro 2013:8) – not support it ‘willy-nilly’.
As Callender (2011:2) says the connection between physics and philosophy has been argued without conclusion over the last hundred years. Therefore, I shall need, not only to consider the philosophy of physics and metaphysics in relation to physics, but also to consider how they should be used in this respect (section 1.3). But before doing so it is necessary to consider arguments on the use of philosophy in contemporary attempts to discover the fundamental processes of the universe. As Aristotle (1923: A§1 and 2) claimed, and I shall argue, theories should follow from a set of first causes, not the other way round. This cause would be responsible for what humans see as laws.
1.1.4 Philosophy versus physics
The arguments raised above appear to have devolved into a struggle between philosophers and physicists perhaps polarizing the two sides, maybe even subliminally leading to the ‘naturalistic’
concept that metaphysics should follow from physics rather than plying an alternative road to an overall theory.
The distinction between ‘philosophy of physics’ and ‘metaphysics’ is not always considered by physicists, the two sometimes being conjoined and then rejected in the physical consideration of natural laws; for example, Weinberg (1993:Ch 7) writes “the teachings of philosophers…[won’t]
provide today's scientists with any useful guidance”. Stenger (2015:1-4) records9 most physicists believe philosophy is only of interest to philosophers; that “observation is the only reliable source of knowledge about the natural world”. A ‘logical positivist’ view originally suggesting that only physics can provide factual knowledge about the universe but now somewhat relaxed in the view that, although observation is the centre of physics, philosophical input is used by physicists in its interpretation. Nevertheless, an extreme stance was taken by Hawking and Mlodinow (2010:13) who declared that “philosophy is dead” because it has not kept up with advances in science, not that this is true: in the philosophical literature there are numerous references to contemporary physics in the form of cosmology, quantum mechanics and field theory10. However, a question rises over the meaning of Hawking and Mlodinow’s bald statement, as indeed of Weinberg and others of the same ilk: Do they accept or refute that the principle of metaphysics was, and still is, the discovery of the fundamental reality of the foundation of the universe? Their statement seems somewhat arrogant in assuming that all the peculiarities of contemporary science are absolute, and philosophy has not been able to particularize these deductions. Or do they mean that philosophical questions concerning the truthfulness of modern science are null and void? They may here have a point: human perception may differ from one person to the next so that many views can be entertained, none of which can ever be regarded as absolute although everyone may appear to agree with apparent observation. There may be more than one explanation for a given set of data (Kuhn 1970:76). The same problem would apply equally to all physical theory.
Against this, de Haro (2013:5) has pointed out that not all of theory is purely scientific; it must consider that theory, even when based on experiment, is an interpretation of the human mind and therefore open to philosophical review. As with Ellis (2012:27-29), Zinkernagel (2011:215,217), or Feyerabend (1993:317), de Haro sees the possibility of philosophical enquiry giving new insights into knowledge. An examination of many of the theories will show that physicists (see e.g., Mermin 1981, EPR 1935, Ellis 2012) adopt philosophical arguments, particularly on aspects of reality. Weinberg in his much cited ‘Against Philosophy’ (1993: Chapter 7) states that physicists use their own philosophy with no need of external sources – often expressed in unintelligible language. He complains that philosophy is a “great danger” because it may cause physicists to question established theories. This is perhaps a strong argument in favour of philosophical questions (see Ellis 2012:27). After all, physicists, possibly more than in any other discipline, are entrenched in ‘accepted’ theories (Bird
9 Stenger in article on discussions by physicists. Krauss, Baggini, Tyson, i.a.
10 See e.g., philosophical articles by Esfeld (2018), Fraser (2018), Myrvold (2014), Dorato and Laudisa (2014), Frigg (2014), Weinstein and Rickles (2015), Vaid (2014), and Ney (2016).
2000:37,45; Duck and Sudarshan 1998:5; Fischbein [1980]1982; Sherin 2006, Ogborn 2011, Feyerabend 1993:164,207) a subject reviewed briefly in section 2.5.3. These ‘accepted theories’ are often without fundamental definitions and assume absoluteness without any form of proof. They cannot even begin to answer questions such as why anything exists, or what mass or electric charge are, or even more fundamentally, what time or space are. As a University of Florida course (2007) says “Some of the simplest questions we ask about things are also the most fundamental and the most difficult to answer. … When [they] go deep enough, they are philosophical in character”; a point that will need to be considered in constructing the arguments formulating a theory of everything, or final theory. By ignoring the philosophical side physicists may be ignoring valuable pointers to unexpected solutions. If we do not know the nature of something, how can we formulate laws about it? A view from Stenlund (2003) is relevant here that when physicists engage in philosophical discussions, they are between physicists using their own mathematical-physical arguments and methodology. External views can provide insights that do not arise through physical observations or mathematical constructions.
Returning to Hawking and Mlodinow, they unintentionally raised, or rather missed, a very important point: physical theories are based on human perception which may vary from individual to individual. If they are not to be tested at an extra-theoretical level how can anyone ‘know for certain’
they are correct. Merely calling them mathematical neglects the problem raised earlier that this depends on both human observation of the universe and interpretation of these observations. The resulting mathematics will only follow the data it is given. There should be an underlying foundation that can be determined as truthful. Here, Immanuel Kant’s problem raises its head: reality must be the primary (a priori) or foundation of existence, but the establishment of such reality can only be made by human thought/perception (Kant [1783]1902: Part3)11. However, there is a partial way round this difficulty, the concept of a self-evident premise. Again, one must veer away from the often-used concept ‘self-evident truth’, due to its self-evidence being purely in human perception/interpretation.
Nevertheless, self-evidence seems the closest we can ever come to truth, provided such a ‘truth’
contains the possibility of a contradiction should it be false. Common reason then suggests a universal foundation should reflect the most basic notions of human perceptions: those of space and time – agreeing with Aristotle’s fundamental causes.
In any case, the nature of reality is not necessarily the first foundation because it depends on the existence, or being, of something in the first place. So, an overarching rule, something that determines foundational reality leading to human observation, must follow from existence. But this creates a
11 Cf. Wilshire and Walsh (2018) who reflect on the concept of knowledge allied to the concept of truth, also cf Carter (2003:159).
